A Mathematical Model for Optimal Tuning Systems

N THIS PAPER WE PROPOSE a mathematical framework for the optimization of tuning systems. We begin with an informal definition of " tuning system. " We then propose five general constraints that seem common to their evolution. The central idea of this paper is the quan-tification of those constraints in terms of a set of numerical parameters. Given a choice of parameter values we use appropriate optimization methods to produce an optimal tuning for a specific set of values. Finally, we consider some historical and Javanese tunings from this perspective , and use the framework to generate a few examples of novel tuning systems.